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Question

Find the tension (in N) acting on 2m mass when the system is released from rest. Assume that the pulleys are ideal and strings are inextensible.

A
24mg29
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B
23mg24
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C
25mg23
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D
23mg25
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Solution

The correct option is A 24mg29
The given system can be reframed as shown

From constrained condition and using method of intercept we get,

a) ..L1+..L2=0a1+ap=0
a1=ap

b) ..L3+..L4=0
a2apap+a3=0
2ap=a3a2
2a1=a3a2.............(1)

From FBD of 2m, 3m and m
3m: 3mgT2=3ma3(2) and T1=2T2(3)
2m: T22mg=2ma2(4)
m: T1mg=ma1(5)

Putting the values of a1, a2 and a3 into eq (1) from (2), (3), (4) and (5) we get

2[2T2mg]=[gT23m][T22mg]
4T2m+T23m+T22m=4gT2=24mg29

Thus, the tension acting on the mass 2m is 24mg29 N

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